Unconfirmed reports are circulating in the US that the 32-year-old actor has asked for Elizabeth's hand in marriage. She has apparently accepted, two weeks after her sister Mary-Kate agreed to wed Olivier Sarkozy.
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Elizabeth, 25, has been dating Boyd for two years. The couple originally met on the set of Very Good Girls in 2012, when onlookers said they had "great chemistry".
They are said to have moved in together in New York a few months ago, setting up home in Brooklyn.
Elizabeth's 27-year-old sister Mary-Kate is yet to confirm her engagement to Olivier – the half brother of former French president Nicolas Sarkozy.
Her huge engagement ring, which made her the centre of attention at Paris fashion Week, did all the talking, however.
The ring in question is thought to be an intricate Cartier piece dating from 1953 — a fitting choice considering the blonde beauty's penchant for vintage clothing.
It features a four-carat central diamond flanked by 16 sapphires, and the "petals" are set with single-cut diamonds.
It was reportedly bought at a Sotheby's auction in New York City for around £48,600, after being originally valued at between £24,000 and £36,000. The ring is said to have belonged to a Tennessee-based jewellery collector.
While engagement reports circle her sisters, Ashley Olsen is also feeling loved-up. Last month sources suggested that Ashley, 27, was dating 47-year-old Moneyball director Bennett Miller.
The couple have been spending lots of time together in LA while Bennett makes the final cuts to his new film and were spotted on a dinner date at Dan Tana's in West Hollywood on 24 January.